This paper addresses the adaptive dynamic output-feedback control problem for a class of nonlinear discrete-time systems with multiple time-varying delays. First, the guaranteed cost function is introduced for the nonlinear system to reduce the effect of the time-varying delays. Secondly, in order to deal with the multiple time-varying delays, the nonlinear system is decomposed into two subsystems. Then the compensator is designed for the first subsystem, and the adaptive dynamic output-feedback controller is constructed based on the subsystems. By introducing the new discrete Lyapunov-Krasovskii functional, it can be seen that the solutions of the resultant closed-loop system converge to an adjustable bounded region. Finally, the simulations are performed to show the effectiveness of the proposed methods.